What is the expected value of this problem?

Question

Four letters are typed at random so that each of the $26$ Latin alphabet letters is equally likely, and the letters are typed independently of one another. What is the expected number of times the word $OF$ appears in this $4$ letter random text?

Answer 1

Let $X$ be the times the word OF appears in this 4 letter random text. It is easy to see that $X$ can be $0$, $1$ or $2$.

$$E(X)=0\cdot P(X=0)+1\cdot P(X=1)+2\cdot P(X=2)=$$

$$=0+1\cdot \frac{(26^2-1)+26^2+(26^2-1)}{26^4}+2\cdot\frac1{26^4}=\frac{3\cdot 26^2}{26^4}=\frac3{676}$$

Answer 2

$$E(X) = 0\cdot P(X=0)+1\cdot P(X=1)+2\cdot P(X=2)$$

$$P(X=1)= {2\over 26^2}-{1\over 26^4} $$

$$P(X=2)= {1\over 26^4}$$